$\"\"$

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Observe the graph:

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The major axis is horizontal.

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The vertices of the ellipse are $\"\"$ and $\"\"$ .

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The co-vertices of the ellipse are $\"\"$ and $\"\"$ .

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Since the major axis is vertical, the standard form of ellipse equation is

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$\"\"$ .

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The center of the ellipse is the mid point of vertices.

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The vertices of the ellipse are $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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The distance between vertices is $\"\"$ .

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Apply the distance between two points formula: $\"\"$ .

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Substitute vertices $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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The distance between co-vertices is $\"\"$ .

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Substitute co-vertices are $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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Substitute $\"\"$ , $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$ .

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The ellipse equation is $\"\"$ .

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$\"\"$

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The ellipse equation is $\"\"$ .